Building Student Success - B.C. Curriculum (2023)

• Sample questions to support inquiry with students:
  • After solving a problem, can we extend it? Can we generalize it?
  • How can we take a contextualized problem and turn it into a mathematical problem that can be solved?
  • How do we tell if a mathematical solution is reasonable?
  • Where can errors occur when solving a contextualized problem?
  • What are the similarities and differences between quadratic functions and linear functions? How are they connected?
  • What do we notice about the rate of change in a quadratic function?
  • How do the strategies for solving linear equations extend to solving quadratic, radical, or rational equations?
  • What is the connection between domain and extraneous roots?

• Sample questions to support inquiry with students:
  • How are the different operations (+, -, x, ÷, exponents, roots) connected?
  • What are the similarities and differences between multiplication of numbers, powers, radicals, polynomials, and rational expressions?
  • How can we verify that we have factored a trinomial correctly?
  • How can visualization support algebraic thinking?
  • How can patterns in numbers lead to algebraic generalizations?
  • When would we choose to represent a number with a radical rather than a rational exponent?
  • How do strategies for factoring x²+bx+cextend to ax² +bx + c, a≠1
  • How do operations on rational numbers extend to operations with rational expressions?

• Sample questions to support inquiry with students:
  • What are some examples of quadratic relationships in the world around us, and what are the similarities and differences between these?
  • Why are quadratic relationships so prevalent in the world around us?
  • How does the predictable pattern of linear functions extend to quadratic functions?
  • Why is the shape of a quadratic function called a parabola?
  • How can we decide which form of a quadratic function to use for a given problem?
  • What effect does each term of a quadratic function have on its graph?

• comparisons of relative size or scale instead of numerical difference

• using measurable values to calculate immeasurable values (e.g., calculating the width of a river using the distance between two points on one shore and an angle to a point on the other shore)
• Sample questions to support inquiry with students:
  • How is the cosine law related to the Pythagorean theorem?
  • How can we use right triangles to find a rule for solving non-right triangles?
  • How do we decide when to use the sine law or cosine law?
  • What would it mean for an angle to have a negative measure? Identify a context for making sense of a negative angle.

real number

• positive and negative rational exponents
• exponent laws
• evaluation using order of operations
• numerical and variable bases

• simplifying radicals
• ordering a set of irrational numbers
• performing operations with radicals
• solving simple (one radical only) equations algebraically and graphically
• identifying domain restrictions and extraneous roots of radical equations

• greatest common factor of a polynomial
• trinomials of the form ax² + bx + c
• difference of squares of the form a²x²- b²y²
• may extend to a(f(x))² + b(f(x)) +c, a²(f(x))² - b²(f(x))²

• simplifying and applying operations to rational expressions
• identifying non-permissible values
• solving equations and identifying any extraneous roots

• identifying characteristics of graphs (including domain and range, intercepts, vertex, symmetry), multiple forms, function notation, extrema
• exploring transformations
• solving equations (e.g., factoring, quadratic formula, completing the square, graphing, square root method)
• connecting equation-solving strategies
• connecting equations with functions
• solving problems in context

• single variable (e.g., 3x - 7 ≤ -4, x² - 5x + 6 > 0)
• domain and range restrictions from problems in situational contexts
• sign analysis: identifying intervals where a function is positive, negative, or zero
• symbolic notation for inequality statements, including interval notation

• use of sine and cosine laws to solve non-right triangles, including ambiguous cases
• contextual and non-contextual problems
• angles in standard position:
  • degrees
  • special angles, as connected with the 30-60-90 and 45-45-90 triangles
• unit circle
• reference and coterminal angles
• terminal arm
• trigonometric ratios
• simple trigonometric equations

• compound interest
• introduction to investments/loans with regular payments, using technology
• buy/lease

• using reason to determine winning strategies
• generalizing and extending

• examine the structure of and connections between mathematical ideas (e.g., trinomial factoring, roots of quadratic equations)

• inductive and deductive reasoning
• predictions, generalizations, conclusions drawn from experiences (e.g., with puzzles, games, and coding)

• graphing technology, dynamic geometry, calculators, virtual manipulatives, concept-based apps
• can be used for a wide variety of purposes, including:
  • exploring and demonstrating mathematical relationships
  • organizing and displaying data
  • generating and testing inductive conjectures
  • mathematical modelling

• manipulatives such as algebra tiles and other concrete materials

• be able to defend the reasonableness of an estimated value or a solution to a problem or equation (e.g., the zeros of a graphed polynomial function)

• includes:
  • using known facts and benchmarks, partitioning, applying whole number strategies to rational numbers and algebraic expressions
  • choosing from different ways to think of a number or operation (e.g., Which will be the most strategic or efficient?)

• use mathematical concepts and tools to solve problems and make decisions (e.g., in real-life and/or abstract scenarios)
• take a complex, essentially non-mathematical scenario and figure out what mathematical concepts and tools are needed to make sense of it

• including real-life scenarios and open-ended challenges that connect mathematics with everyday life

• by being open to trying different strategies
• refers to creative and innovative mathematical thinking rather than to representing math in a creative way, such as through art or music

• asking questions to further understanding or to open other avenues of investigation

• includes structured, guided, and open inquiry
• noticing and wondering
• determining what is needed to make sense of and solve problems

• create and use mental images to support understanding
• Visualization can be supported using dynamic materials (e.g., graphical relationships and simulations), concrete materials, drawings, and diagrams.

• deciding which mathematical tools to use to solve a problem
• choosing an effective strategy to solve a problem (e.g., guess and check, model, solve a simpler problem, use a chart, use diagrams, role-play)

• interpret a situation to identify a problem
• apply mathematics to solve the problem
• analyze and evaluate the solution in terms of the initial context
• repeat this cycle until a solution makes sense

Solve problems with persistence and a positive disposition

• through daily activities, local and traditional practices, popular media and news events, cross-curricular integration
• by posing and solving problems or asking questions about place, stories, and cultural practices

• use mathematical arguments to convince
• includes anticipating consequences

• Have students explore which of two scenarios they would choose and then defend their choice.

• including oral, written, visual, use of technology
• communicating effectively according to what is being communicated and to whom

• using models, tables, graphs, words, numbers, symbols
• connecting meanings among various representations

• partner talks, small-group discussions, teacher-student conferences

• is valuable for deepening understanding of concepts
• can help clarify students’ thinking, even if they are not sure about an idea or have misconceptions

• share the mathematical thinking of self and others, including evaluating strategies and solutions, extending, posing new problems and questions

• to develop a sense of how mathematics helps us understand ourselves and the world around us (e.g., daily activities, local and traditional practices, popular media and news events, social justice, cross-curricular integration)

• range from calculation errors to misconceptions

• by:
  • analyzing errors to discover misunderstandings
  • making adjustments in further attempts
  • identifying not only mistakes but also parts of a solution that are correct

• by:
  • collaborating with Elders and knowledge keepers among local First Peoples
  • exploring the First Peoples Principles of Learning (http://www.fnesc.ca/wp/wp-content/uploads/2015/09/PUB-LFP-POSTER-Princi…; e.g., Learning is holistic, reflexive, reflective, experiential, and relational [focused on connectedness, on reciprocal relationships, and a sense of place]; Learning involves patience and time)
  • making explicit connections with learning mathematics
  • exploring cultural practices and knowledge of local First Peoples and identifying mathematical connections

• local knowledge and cultural practices that are appropriate to share and that are non-appropriated

• Bishop’s cultural practices: counting, measuring, locating, designing, playing, explaining (http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/abishop.htm)
• Aboriginal Education Resources (www.aboriginaleducation.ca)
• Teaching Mathematics in a First Nations Context, FNESC (http://www.fnesc.ca/resources/math-first-peoples/)